More than 2,700 schools in England will need to improve kitchens to provide free meals for infant school children, according to new figures.
Freedom of Information figures obtained by the BBC found this to be about one in three schools assessed so far.
Deputy Prime Minister Nick Clegg announced the policy at last year's Liberal Democrat conference.
The Department for Education has provided funding for improvements and said it is offering support to schools.
According to the most recent figures from January 2012, there are more than 16,800 state primary schools in England.
The work needed ranges from a new microwave or dishwasher to a full refurbishment.
The figures also showed that more than 1,700 schools had no kitchen at all.
These will have hot meals delivered by external caterers, or cooked at neighbouring schools and transported in as many currently do.
Some of the 152 local authorities who provided information said their funding allocation was adequate to make necessary improvements, others said it fell short of estimated costs.
In many schools lunchtimes will be staggered or extended in order to seat all pupils in small halls.
Schools Minister David Laws told BBC Radio 4's Today programme he was "not complacent" about the problems, but a service set up to help introduce the policy was "yet to find a school that with the right support and advice cannot actually deal with these issues".
"The anecdotal evidence and the noise that you tend to get will tend to be from what can sometimes be a small minority of schools, and I take their concerns seriously," he said.
"But what you don't hear about, and what I do hear about, is the vast majority of schools that are on track to deliver this."
Critics say the deputy prime minister's policy was rushed through and is proving to hard to implement. Some schools may have to offer sandwiches in September instead of hot meals.
'Shown to work'
A Department for Education spokesman said: "School lunches for all infant children will save parents money, improve children's education and make sure more children eat a healthy and nutritious meal at least once a day.
"Universal free school meals have already been shown to work in the pilot schemes run by the Department for Education and Department of Health in 2009.
"Indeed, schools have had longer to prepare for the introduction of universal free school meals this September than schools in those pilot areas had in 2009.
"Schools are receiving a huge amount of support to provide free school meals. We are providing £150m to improve kitchens and dining facilities, as well as an additional £22.5m specifically to help smaller schools to provide these meals."
Under the scheme, all Reception, Year 1 and Year 2 children in state-funded schools in England will be entitled to free school meals from September.